Question

Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

Answer 1

Given lines are, 

3x + y – 2 = 0  ………………. (1) 

px + 2y – 3 = 0 …………………… (2) 

2x – y – 3 = 0  ……………….. (3) 

Now, solve (1) and (3): we get 5x – 5 = 0 ⇒ x = 1 

Using x = 1 on (1), we get y = -1 

Point of intersection of (1) and (3) is U,y) = (1, - 1) 

The three lines are concurrent if the point (1,-1) lies on (2). 

i.e., p( 1) + 2(-1) - 3 = 0 

⇒ p = 5